The sum of the present ages of a father and his son is 70 years. Five years ago, the age of the father was five times the age of the son. What is the present age of the son in years?

Introduction / Context:
This is a classic aptitude question from the topic of problems on ages. We are given the sum of the present ages of a father and his son and a condition relating their ages five years ago. Using this information, we need to determine the present age of the son in years. Such questions commonly appear in competitive exams and are solved using simple linear equations based on present, past, and future ages.

Given Data / Assumptions:
The sum of the present ages of the father and the son is 70 years. Five years ago, the age of the father was five times the age of the son. Ages are assumed to be whole numbers in years. We are asked to find the present age of the son.

Concept / Approach:
Problems on ages are usually solved by expressing all conditions in terms of present ages and then forming linear equations. When the statement says "five years ago", we subtract 5 from the present age. Ratios or multipliers such as "five times" are then used to relate the ages. Solving the resulting equations gives the required present age.

Step-by-Step Solution:
Step 1: Let the present age of the son be S years and the present age of the father be F years.Step 2: From the sum condition, F + S = 70.Step 3: Five years ago, the father's age was F - 5 and the son's age was S - 5. At that time, F - 5 = 5 * (S - 5).Step 4: Expand the second equation: F - 5 = 5S - 25, so F = 5S - 20.Step 5: Substitute F = 5S - 20 into F + S = 70 to get (5S - 20) + S = 70.Step 6: Simplify: 6S - 20 = 70, so 6S = 90 and S = 15.Step 7: Therefore, the present age of the son is 15 years.

Verification / Alternative check:
If the son is 15 years old now, the father is 70 - 15 = 55 years old now. Five years ago, the son was 10 years old and the father was 50 years old. At that time, 50 is exactly 5 times 10, so the given condition is satisfied. This confirms that the solution is consistent and correct.

Why Other Options Are Wrong:
If the son were 12 years old, the father would be 58 years old, and five years ago their ages would be 7 and 53, which does not satisfy a five times relationship. If the son were 14 years old, the father would be 56 years old, and five years ago they would be 9 and 51, which again is not a five times relation. If the son were 19 years old, the father would be 51 years old, and five years ago the ages would be 14 and 46, which also does not give a five times ratio. Thus, these options are incorrect.

Common Pitfalls:
A common mistake is to apply the "five times" condition to the present ages instead of the ages five years ago. Another error is to forget that both ages are reduced by 5 when going back five years. Some learners also mis-handle the algebra while substituting one equation into another. Writing the equations carefully and checking the arithmetic step by step helps avoid these issues.

Final Answer:
The present age of the son is 15 years.